Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(61,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.u (of order \(9\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 3 x^{17} + 21 x^{16} - 30 x^{15} + 192 x^{14} - 207 x^{13} + 1178 x^{12} - 705 x^{11} + 4413 x^{10} - 2224 x^{9} + 11430 x^{8} - 4101 x^{7} + 19237 x^{6} - 7125 x^{5} + \cdots + 5329 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 101.3 | ||
Root | \(1.55777 - 2.69813i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.101 |
Dual form | 380.2.u.b.301.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(e\left(\frac{7}{9}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.92764 | + | 1.06558i | 1.69028 | + | 0.615210i | 0.994660 | − | 0.103204i | \(-0.0329093\pi\) |
0.695616 | + | 0.718414i | \(0.255132\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.173648 | + | 0.984808i | 0.0776578 | + | 0.440419i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.643760 | − | 1.11502i | 0.243318 | − | 0.421440i | −0.718339 | − | 0.695693i | \(-0.755097\pi\) |
0.961657 | + | 0.274253i | \(0.0884307\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.13752 | + | 4.31089i | 1.71251 | + | 1.43696i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.25088 | − | 3.89864i | −0.678666 | − | 1.17548i | −0.975383 | − | 0.220518i | \(-0.929225\pi\) |
0.296717 | − | 0.954965i | \(-0.404108\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.115094 | + | 0.0418907i | −0.0319213 | + | 0.0116184i | −0.357931 | − | 0.933748i | \(-0.616518\pi\) |
0.326010 | + | 0.945366i | \(0.394296\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.541007 | + | 3.06820i | −0.139687 | + | 0.792206i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.730551 | + | 0.613005i | −0.177185 | + | 0.148676i | −0.727067 | − | 0.686567i | \(-0.759117\pi\) |
0.549882 | + | 0.835242i | \(0.314673\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.18925 | + | 4.19353i | −0.272834 | + | 0.962061i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.07284 | − | 2.57842i | 0.670549 | − | 0.562658i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.507981 | − | 2.88091i | 0.105921 | − | 0.600710i | −0.884927 | − | 0.465730i | \(-0.845792\pi\) |
0.990848 | − | 0.134980i | \(-0.0430971\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.939693 | + | 0.342020i | −0.187939 | + | 0.0684040i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.77395 | + | 10.0008i | 1.11120 | + | 1.92465i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.12896 | − | 4.30371i | −0.952425 | − | 0.799179i | 0.0272796 | − | 0.999628i | \(-0.491316\pi\) |
−0.979704 | + | 0.200449i | \(0.935760\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.91189 | + | 5.04355i | −0.522991 | + | 0.905847i | 0.476651 | + | 0.879093i | \(0.341851\pi\) |
−0.999642 | + | 0.0267547i | \(0.991483\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.43548 | − | 13.8123i | −0.423963 | − | 2.40441i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.20987 | + | 0.440358i | 0.204506 | + | 0.0744340i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.95982 | −1.47299 | −0.736493 | − | 0.676445i | \(-0.763520\pi\) | ||||
−0.736493 | + | 0.676445i | \(0.763520\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.381591 | −0.0611035 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.45930 | + | 2.71496i | 1.16495 | + | 0.424006i | 0.850862 | − | 0.525389i | \(-0.176080\pi\) |
0.314085 | + | 0.949395i | \(0.398302\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.65520 | − | 9.38710i | −0.252415 | − | 1.43152i | −0.802621 | − | 0.596490i | \(-0.796562\pi\) |
0.550205 | − | 0.835030i | \(-0.314550\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.35328 | + | 5.80804i | −0.499877 | + | 0.865812i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.709210 | − | 0.595097i | −0.103449 | − | 0.0868039i | 0.589596 | − | 0.807698i | \(-0.299287\pi\) |
−0.693045 | + | 0.720894i | \(0.743731\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.67115 | + | 4.62656i | 0.381592 | + | 0.660937i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.79200 | + | 1.01620i | −0.390958 | + | 0.142297i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.00414149 | + | 0.0234876i | −0.000568878 | + | 0.00322627i | −0.985091 | − | 0.172035i | \(-0.944966\pi\) |
0.984522 | + | 0.175261i | \(0.0560770\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.44855 | − | 2.89368i | 0.465002 | − | 0.390183i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.95023 | + | 11.0099i | −1.05303 | + | 1.45830i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.19663 | − | 6.87779i | 1.06711 | − | 0.895411i | 0.0723223 | − | 0.997381i | \(-0.476959\pi\) |
0.994787 | + | 0.101970i | \(0.0325145\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.02491 | − | 5.81255i | 0.131226 | − | 0.744221i | −0.846187 | − | 0.532886i | \(-0.821108\pi\) |
0.977414 | − | 0.211335i | \(-0.0677813\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.11408 | − | 2.95328i | 1.02228 | − | 0.372079i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0612401 | − | 0.106071i | −0.00759590 | − | 0.0131565i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0876 | + | 10.1427i | 1.47673 | + | 1.23913i | 0.909589 | + | 0.415509i | \(0.136397\pi\) |
0.567145 | + | 0.823618i | \(0.308048\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.55701 | − | 7.89297i | 0.548600 | − | 0.950202i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.62142 | − | 14.8668i | −0.311106 | − | 1.76437i | −0.593271 | − | 0.805003i | \(-0.702164\pi\) |
0.282165 | − | 0.959366i | \(-0.408947\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.61254 | + | 1.31486i | 0.422816 | + | 0.153892i | 0.544660 | − | 0.838657i | \(-0.316659\pi\) |
−0.121844 | + | 0.992549i | \(0.538881\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.11553 | −0.359751 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.79610 | −0.660527 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.80162 | − | 1.01971i | −0.315207 | − | 0.114726i | 0.179572 | − | 0.983745i | \(-0.442529\pi\) |
−0.494779 | + | 0.869019i | \(0.664751\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.75375 | + | 15.6173i | 0.305972 | + | 1.73525i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.36455 | + | 7.55962i | −0.479071 | + | 0.829776i | −0.999712 | − | 0.0240000i | \(-0.992360\pi\) |
0.520641 | + | 0.853776i | \(0.325693\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.730551 | − | 0.613005i | −0.0792394 | − | 0.0664897i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.4299 | − | 18.0650i | −1.11820 | − | 1.93677i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.0616 | + | 5.11801i | −1.49053 | + | 0.542508i | −0.953588 | − | 0.301113i | \(-0.902642\pi\) |
−0.536939 | + | 0.843621i | \(0.680420\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0273836 | + | 0.155300i | −0.00287058 | + | 0.0162799i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.8993 | + | 11.6629i | −1.44129 | + | 1.20938i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.33633 | − | 0.442988i | −0.444898 | − | 0.0454496i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.3023 | + | 11.1620i | −1.35064 | + | 1.13332i | −0.371891 | + | 0.928276i | \(0.621291\pi\) |
−0.978752 | + | 0.205048i | \(0.934265\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.24266 | − | 29.7326i | 0.526907 | − | 2.98824i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.82879 | − | 2.48548i | 0.679490 | − | 0.247314i | 0.0208616 | − | 0.999782i | \(-0.493359\pi\) |
0.658629 | + | 0.752468i | \(0.271137\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.425234 | − | 0.736527i | −0.0418996 | − | 0.0725722i | 0.844315 | − | 0.535847i | \(-0.180008\pi\) |
−0.886215 | + | 0.463275i | \(0.846674\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.07284 | + | 2.57842i | 0.299879 | + | 0.251628i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.04809 | − | 8.74355i | 0.488017 | − | 0.845271i | −0.511888 | − | 0.859052i | \(-0.671054\pi\) |
0.999905 | + | 0.0137816i | \(0.00438695\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.521529 | − | 2.95774i | −0.0499534 | − | 0.283300i | 0.949591 | − | 0.313492i | \(-0.101499\pi\) |
−0.999544 | + | 0.0301927i | \(0.990388\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −26.2312 | − | 9.54737i | −2.48975 | − | 0.906196i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.06424 | −0.570475 | −0.285238 | − | 0.958457i | \(-0.592073\pi\) | ||||
−0.285238 | + | 0.958457i | \(0.592073\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.92535 | 0.272790 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.771882 | − | 0.280942i | −0.0713605 | − | 0.0259731i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.213216 | + | 1.20921i | 0.0195455 | + | 0.110848i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.63292 | + | 8.02445i | −0.421174 | + | 0.729496i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.9452 | + | 15.8969i | 1.70823 | + | 1.43337i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.500000 | − | 0.866025i | −0.0447214 | − | 0.0774597i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.24161 | + | 2.27176i | −0.553854 | + | 0.201586i | −0.603758 | − | 0.797168i | \(-0.706331\pi\) |
0.0499042 | + | 0.998754i | \(0.484108\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.15683 | − | 29.2458i | 0.454033 | − | 2.57495i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.06862 | − | 5.93127i | 0.617588 | − | 0.518218i | −0.279456 | − | 0.960158i | \(-0.590154\pi\) |
0.897044 | + | 0.441941i | \(0.145710\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.91029 | + | 4.02567i | 0.339065 | + | 0.349070i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.84620 | + | 7.42284i | −0.761359 | + | 0.638856i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.634270 | + | 3.59712i | −0.0541893 | + | 0.307323i | −0.999840 | − | 0.0178599i | \(-0.994315\pi\) |
0.945651 | + | 0.325183i | \(0.105426\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.6900 | − | 6.43863i | 1.50044 | − | 0.546117i | 0.544269 | − | 0.838911i | \(-0.316807\pi\) |
0.956176 | + | 0.292794i | \(0.0945849\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.44219 | − | 2.49795i | −0.121454 | − | 0.210365i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.422379 | + | 0.354418i | 0.0353211 | + | 0.0296379i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.34769 | − | 5.79837i | 0.278011 | − | 0.481529i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.89022 | + | 16.3912i | 0.238381 | + | 1.35193i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.0670 | − | 4.02805i | −0.906641 | − | 0.329990i | −0.153730 | − | 0.988113i | \(-0.549129\pi\) |
−0.752911 | + | 0.658122i | \(0.771351\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.94029 | 0.564793 | 0.282396 | − | 0.959298i | \(-0.408871\pi\) | ||||
0.282396 | + | 0.959298i | \(0.408871\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.39581 | −0.517071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.47257 | − | 1.99185i | −0.439567 | − | 0.159989i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.03157 | + | 17.1929i | 0.241946 | + | 1.37214i | 0.827480 | + | 0.561495i | \(0.189774\pi\) |
−0.585534 | + | 0.810648i | \(0.699115\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.0371526 | + | 0.0643502i | −0.00294639 | + | 0.00510330i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.88526 | − | 2.42102i | −0.227391 | − | 0.190803i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.12605 | + | 10.6106i | 0.479829 | + | 0.831089i | 0.999732 | − | 0.0231364i | \(-0.00736520\pi\) |
−0.519903 | + | 0.854225i | \(0.674032\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.1796 | − | 4.79696i | 1.02603 | − | 0.373443i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.09639 | + | 23.2318i | −0.316988 | + | 1.79773i | 0.243860 | + | 0.969811i | \(0.421586\pi\) |
−0.560848 | + | 0.827919i | \(0.689525\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.94709 | + | 8.34660i | −0.765160 | + | 0.642046i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.1876 | + | 16.4176i | −1.84968 | + | 1.25548i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.98365 | + | 6.69908i | −0.606986 | + | 0.509321i | −0.893683 | − | 0.448700i | \(-0.851887\pi\) |
0.286697 | + | 0.958021i | \(0.407443\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.223575 | + | 1.26796i | −0.0169007 | + | 0.0958487i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 31.3256 | − | 11.4016i | 2.35458 | − | 0.856996i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.20212 | − | 7.27829i | −0.314081 | − | 0.544005i | 0.665160 | − | 0.746701i | \(-0.268363\pi\) |
−0.979242 | + | 0.202696i | \(0.935030\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.2650 | + | 14.4870i | 1.28329 | + | 1.07681i | 0.992781 | + | 0.119940i | \(0.0382703\pi\) |
0.290513 | + | 0.956871i | \(0.406174\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.19428 | − | 15.9250i | 0.679661 | − | 1.17721i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.55586 | − | 8.82370i | −0.114389 | − | 0.648732i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.03427 | + | 1.46835i | 0.295015 | + | 0.107377i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.8681 | 1.08150 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.2967 | 1.75805 | 0.879025 | − | 0.476775i | \(-0.158194\pi\) | ||||
0.879025 | + | 0.476775i | \(0.158194\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.36570 | + | 1.58898i | 0.314250 | + | 0.114378i | 0.494330 | − | 0.869274i | \(-0.335413\pi\) |
−0.180080 | + | 0.983652i | \(0.557636\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.0662626 | − | 0.375794i | −0.00474516 | − | 0.0269112i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00361 | − | 10.3986i | 0.427740 | − | 0.740867i | −0.568932 | − | 0.822384i | \(-0.692643\pi\) |
0.996672 | + | 0.0815174i | \(0.0259766\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.96006 | + | 7.51838i | 0.635162 | + | 0.532964i | 0.902528 | − | 0.430631i | \(-0.141709\pi\) |
−0.267366 | + | 0.963595i | \(0.586153\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 24.5804 | + | 42.5744i | 1.73376 | + | 3.00297i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.10057 | + | 2.94836i | −0.568548 | + | 0.206935i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.37842 | + | 7.81742i | −0.0962732 | + | 0.545993i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.0290 | − | 12.6108i | 1.04459 | − | 0.876515i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.0259 | − | 4.80266i | 1.31605 | − | 0.332207i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.63682 | − | 8.08626i | 0.663426 | − | 0.556681i | −0.247685 | − | 0.968841i | \(-0.579670\pi\) |
0.911112 | + | 0.412160i | \(0.135225\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.16713 | − | 46.3181i | 0.559603 | − | 3.17367i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.95707 | − | 3.26011i | 0.610867 | − | 0.222337i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.74912 | + | 6.49366i | 0.254507 | + | 0.440819i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.17515 | + | 7.69887i | 0.619999 | + | 0.520241i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0584026 | − | 0.101156i | 0.00392858 | − | 0.00680451i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.34163 | + | 13.2801i | 0.156807 | + | 0.889299i | 0.957115 | + | 0.289709i | \(0.0935586\pi\) |
−0.800307 | + | 0.599590i | \(0.795330\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.30210 | − | 2.29378i | −0.420140 | − | 0.152918i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.1090 | −1.40105 | −0.700526 | − | 0.713627i | \(-0.747051\pi\) | ||||
−0.700526 | + | 0.713627i | \(0.747051\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.3629 | −1.27954 | −0.639770 | − | 0.768567i | \(-0.720970\pi\) | ||||
−0.639770 | + | 0.768567i | \(0.720970\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.9689 | − | 6.17619i | −1.11647 | − | 0.406363i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.321621 | − | 1.82400i | −0.0210701 | − | 0.119494i | 0.972459 | − | 0.233075i | \(-0.0748789\pi\) |
−0.993529 | + | 0.113581i | \(0.963768\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.462904 | − | 0.801773i | 0.0301965 | − | 0.0523019i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.11558 | − | 5.97068i | −0.462207 | − | 0.387837i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.6784 | + | 18.4956i | 0.690730 | + | 1.19638i | 0.971599 | + | 0.236633i | \(0.0760441\pi\) |
−0.280869 | + | 0.959746i | \(0.590623\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.67933 | − | 2.06711i | 0.365838 | − | 0.133154i | −0.152559 | − | 0.988294i | \(-0.548751\pi\) |
0.518397 | + | 0.855140i | \(0.326529\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.56358 | + | 14.5388i | −0.164454 | + | 0.932663i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.09243 | + | 3.43396i | −0.261456 | + | 0.219388i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0387941 | − | 0.532467i | −0.00246841 | − | 0.0338801i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −20.8332 | + | 17.4811i | −1.32025 | + | 1.10782i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.425210 | + | 2.41149i | −0.0268390 | + | 0.152212i | −0.995282 | − | 0.0970230i | \(-0.969068\pi\) |
0.968443 | + | 0.249235i | \(0.0801791\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.3750 | + | 4.50414i | −0.778010 | + | 0.283173i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.48559 | − | 2.57312i | −0.0930313 | − | 0.161135i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.75878 | + | 6.51039i | 0.483979 | + | 0.406107i | 0.851863 | − | 0.523765i | \(-0.175473\pi\) |
−0.367884 | + | 0.929872i | \(0.619917\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.76798 | + | 9.99043i | −0.358405 | + | 0.620775i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.79732 | − | 44.2208i | −0.482642 | − | 2.73720i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.3651 | − | 3.77260i | −0.639141 | − | 0.232628i | 0.00206405 | − | 0.999998i | \(-0.499343\pi\) |
−0.641205 | + | 0.767370i | \(0.721565\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.0238499 | −0.00146509 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −46.6210 | −2.85316 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.7568 | + | 6.82690i | 1.14362 | + | 0.416243i | 0.843219 | − | 0.537570i | \(-0.180658\pi\) |
0.300400 | + | 0.953813i | \(0.402880\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.988320 | − | 5.60504i | −0.0600362 | − | 0.340482i | 0.939964 | − | 0.341275i | \(-0.110859\pi\) |
−1.00000 | 0.000792933i | \(0.999748\pi\) | ||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.245653 | + | 0.425484i | −0.0148676 | + | 0.0257514i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.44855 | + | 2.89368i | 0.207955 | + | 0.174495i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.0854 | − | 27.8607i | −0.966477 | − | 1.67399i | −0.705594 | − | 0.708616i | \(-0.749320\pi\) |
−0.260883 | − | 0.965370i | \(-0.584014\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −36.7021 | + | 13.3585i | −2.19729 | + | 0.799750i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.33744 | − | 13.2563i | 0.139440 | − | 0.790805i | −0.832224 | − | 0.554440i | \(-0.812933\pi\) |
0.971664 | − | 0.236365i | \(-0.0759563\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.76933 | − | 4.84104i | 0.342951 | − | 0.287770i | −0.455001 | − | 0.890491i | \(-0.650361\pi\) |
0.797952 | + | 0.602721i | \(0.205917\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −12.2232 | − | 5.91760i | −0.724040 | − | 0.350528i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.82925 | − | 6.56952i | 0.462146 | − | 0.387787i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.79409 | + | 15.8461i | −0.164358 | + | 0.932122i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −50.8383 | + | 18.5036i | −2.98019 | + | 1.08470i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.3915 | + | 21.4627i | 0.723919 | + | 1.25386i | 0.959418 | + | 0.281989i | \(0.0909942\pi\) |
−0.235499 | + | 0.971875i | \(0.575672\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.19663 | + | 6.87779i | 0.477226 | + | 0.400440i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 25.9929 | − | 45.0210i | 1.50826 | − | 2.61239i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.0622176 | + | 0.352854i | 0.00359814 | + | 0.0204061i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.5324 | − | 4.19745i | −0.664717 | − | 0.241937i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.6407 | 1.30068 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.90222 | 0.337960 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.1933 | + | 5.89388i | 0.924200 | + | 0.336381i | 0.759908 | − | 0.650031i | \(-0.225244\pi\) |
0.164292 | + | 0.986412i | \(0.447466\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.460109 | − | 2.60941i | −0.0261747 | − | 0.148444i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.22506 | − | 7.31802i | 0.239581 | − | 0.414967i | −0.721013 | − | 0.692922i | \(-0.756323\pi\) |
0.960594 | + | 0.277955i | \(0.0896565\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.13129 | + | 0.949265i | 0.0639443 | + | 0.0536556i | 0.674200 | − | 0.738549i | \(-0.264489\pi\) |
−0.610255 | + | 0.792205i | \(0.708933\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.31741 | + | 7.47797i | 0.243258 | + | 0.421336i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.10586 | + | 0.766472i | −0.118277 | + | 0.0430494i | −0.400481 | − | 0.916305i | \(-0.631157\pi\) |
0.282204 | + | 0.959355i | \(0.408935\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.23393 | + | 29.6831i | −0.293044 | + | 1.66193i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.0959 | − | 20.2189i | 1.34490 | − | 1.12851i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.70184 | − | 3.79260i | −0.0946931 | − | 0.211026i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0938253 | − | 0.0787287i | 0.00520449 | − | 0.00436708i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.62484 | − | 9.21493i | 0.0898539 | − | 0.509587i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.12011 | + | 0.407686i | −0.0617536 | + | 0.0224765i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.35657 | − | 2.34964i | −0.0745637 | − | 0.129148i | 0.826333 | − | 0.563182i | \(-0.190423\pi\) |
−0.900896 | + | 0.434034i | \(0.857090\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −46.0313 | − | 38.6248i | −2.52250 | − | 2.11663i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.88961 | + | 13.6652i | −0.431056 | + | 0.746610i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.01515 | + | 11.4285i | 0.109772 | + | 0.622549i | 0.989206 | + | 0.146529i | \(0.0468101\pi\) |
−0.879434 | + | 0.476020i | \(0.842079\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.7539 | − | 6.46190i | −0.964261 | − | 0.350962i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.2173 | 1.41975 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.8909 | 0.858030 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.56438 | + | 3.11718i | 0.461091 | + | 0.167823i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.33836 | − | 30.2754i | −0.286578 | − | 1.62527i | −0.699593 | − | 0.714542i | \(-0.746635\pi\) |
0.413014 | − | 0.910725i | \(-0.364476\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.56699 | − | 16.5705i | 0.512109 | − | 0.886999i | −0.487792 | − | 0.872960i | \(-0.662198\pi\) |
0.999901 | − | 0.0140393i | \(-0.00446900\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.08348 | − | 0.909151i | −0.0578321 | − | 0.0485269i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.74328 | − | 16.8759i | −0.518583 | − | 0.898211i | −0.999767 | − | 0.0215918i | \(-0.993127\pi\) |
0.481184 | − | 0.876619i | \(-0.340207\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.1858 | − | 5.16320i | 0.752902 | − | 0.274034i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.664283 | + | 3.76734i | −0.0351576 | + | 0.199389i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.7000 | + | 21.5649i | −1.35639 | + | 1.13815i | −0.379317 | + | 0.925267i | \(0.623841\pi\) |
−0.977078 | + | 0.212884i | \(0.931714\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.1714 | − | 9.97434i | −0.851124 | − | 0.524965i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −22.1142 | + | 18.5560i | −1.16069 | + | 0.973938i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.667571 | + | 3.78598i | −0.0349422 | + | 0.198167i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.1767 | + | 3.70401i | −0.531219 | + | 0.193348i | −0.593683 | − | 0.804699i | \(-0.702327\pi\) |
0.0624636 | + | 0.998047i | \(0.480104\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 26.6184 | + | 46.1044i | 1.38570 | + | 2.40010i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.0235231 | + | 0.0197382i | 0.00122126 | + | 0.00102476i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.14975 | + | 7.18758i | −0.214866 | + | 0.372159i | −0.953231 | − | 0.302242i | \(-0.902265\pi\) |
0.738365 | + | 0.674401i | \(0.235598\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.541007 | − | 3.06820i | −0.0279375 | − | 0.158441i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.770597 | + | 0.280474i | 0.0396878 | + | 0.0144452i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.75557 | 0.141544 | 0.0707720 | − | 0.997493i | \(-0.477454\pi\) | ||||
0.0707720 | + | 0.997493i | \(0.477454\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.6940 | −1.06018 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.15130 | + | 0.783010i | 0.109926 | + | 0.0400100i | 0.396398 | − | 0.918079i | \(-0.370260\pi\) |
−0.286471 | + | 0.958089i | \(0.592482\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.00648 | − | 5.70805i | −0.0512951 | − | 0.290909i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 31.9631 | − | 55.3618i | 1.62478 | − | 2.81420i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.46044 | − | 7.09915i | −0.428961 | − | 0.359941i | 0.402598 | − | 0.915377i | \(-0.368107\pi\) |
−0.831560 | + | 0.555436i | \(0.812552\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.39490 | + | 2.41604i | 0.0705433 | + | 0.122185i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 27.0146 | − | 9.83252i | 1.36271 | − | 0.495985i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.517719 | − | 2.93613i | 0.0260493 | − | 0.147733i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.4339 | + | 12.1114i | −0.724415 | + | 0.607856i | −0.928603 | − | 0.371076i | \(-0.878989\pi\) |
0.204188 | + | 0.978932i | \(0.434545\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.15829 | + | 15.9525i | 0.358363 | + | 0.798621i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.34821 | − | 1.13128i | 0.0673263 | − | 0.0564935i | −0.608503 | − | 0.793551i | \(-0.708230\pi\) |
0.675830 | + | 0.737058i | \(0.263785\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.123863 | − | 0.702462i | 0.00617005 | − | 0.0349921i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −14.9018 | + | 5.42382i | −0.740478 | + | 0.269512i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.1675 | + | 34.9311i | 0.999665 | + | 1.73147i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.30115 | − | 7.80459i | −0.459912 | − | 0.385912i | 0.383187 | − | 0.923671i | \(-0.374827\pi\) |
−0.843099 | + | 0.537759i | \(0.819271\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.68992 | + | 9.85523i | −0.280663 | + | 0.486123i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.39224 | − | 13.5671i | −0.117715 | − | 0.667593i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.20267 | − | 2.98553i | −0.402653 | − | 0.146554i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 58.6508 | 2.87214 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.4679 | −0.804509 | −0.402255 | − | 0.915528i | \(-0.631773\pi\) | ||||
−0.402255 | + | 0.915528i | \(0.631773\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.999150 | + | 0.363661i | 0.0486956 | + | 0.0177237i | 0.366253 | − | 0.930515i | \(-0.380640\pi\) |
−0.317558 | + | 0.948239i | \(0.602863\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.07818 | − | 6.11465i | −0.0524228 | − | 0.297304i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.476833 | − | 0.825899i | 0.0231298 | − | 0.0400620i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.82134 | − | 4.88469i | −0.281715 | − | 0.236387i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.858916 | + | 1.48769i | 0.0414688 | + | 0.0718261i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.7978 | − | 11.9374i | 1.57982 | − | 0.575006i | 0.604651 | − | 0.796490i | \(-0.293312\pi\) |
0.975164 | + | 0.221484i | \(0.0710902\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.23492 | + | 7.00358i | −0.0593465 | + | 0.336571i | −0.999996 | − | 0.00280872i | \(-0.999106\pi\) |
0.940650 | + | 0.339379i | \(0.110217\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.9795 | − | 13.4084i | 0.766156 | − | 0.642882i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.4770 | + | 5.55636i | 0.549021 | + | 0.265797i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.83392 | + | 4.89524i | −0.278438 | + | 0.233637i | −0.771302 | − | 0.636469i | \(-0.780394\pi\) |
0.492864 | + | 0.870106i | \(0.335950\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.22153 | + | 35.2841i | −0.296263 | + | 1.68019i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.2738 | + | 5.92317i | −0.773191 | + | 0.281419i | −0.698330 | − | 0.715776i | \(-0.746073\pi\) |
−0.0748605 | + | 0.997194i | \(0.523851\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.48203 | − | 12.9592i | −0.354682 | − | 0.614327i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −28.1080 | − | 23.5854i | −1.32946 | − | 1.11555i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.462444 | − | 0.800976i | 0.0218241 | − | 0.0378004i | −0.854907 | − | 0.518781i | \(-0.826386\pi\) |
0.876731 | + | 0.480981i | \(0.159719\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.20533 | − | 35.1922i | −0.292197 | − | 1.65713i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.3187 | + | 7.39540i | 0.954656 | + | 0.347466i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.157696 | −0.00739289 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.6874 | −0.967718 | −0.483859 | − | 0.875146i | \(-0.660765\pi\) | ||||
−0.483859 | + | 0.875146i | \(0.660765\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.3487 | − | 3.76661i | −0.483035 | − | 0.175810i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.46202 | + | 13.9628i | 0.114667 | + | 0.650312i | 0.986914 | + | 0.161246i | \(0.0515512\pi\) |
−0.872247 | + | 0.489066i | \(0.837338\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.7765 | − | 32.5218i | 0.872616 | − | 1.51141i | 0.0133346 | − | 0.999911i | \(-0.495755\pi\) |
0.859281 | − | 0.511504i | \(-0.170911\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.8993 | − | 11.6629i | −0.644563 | − | 0.540852i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.95532 | + | 5.11877i | 0.136756 | + | 0.236868i | 0.926267 | − | 0.376868i | \(-0.122999\pi\) |
−0.789511 | + | 0.613736i | \(0.789666\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.0909 | − | 6.94850i | 0.881534 | − | 0.320852i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.44497 | + | 53.5651i | −0.435201 | + | 2.46815i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −32.8713 | + | 27.5823i | −1.51142 | + | 1.26823i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.316738 | − | 4.34738i | −0.0145329 | − | 0.199471i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.122529 | + | 0.102814i | −0.00561023 | + | 0.00470755i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.61205 | − | 9.14240i | 0.0736565 | − | 0.417727i | −0.925576 | − | 0.378561i | \(-0.876419\pi\) |
0.999233 | − | 0.0391656i | \(-0.0124700\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.03122 | − | 0.375333i | 0.0470196 | − | 0.0171137i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.86724 | − | 10.1624i | −0.266969 | − | 0.462403i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.3023 | − | 11.1620i | −0.604026 | − | 0.506838i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.4983 | − | 21.6477i | 0.566353 | − | 0.980951i | −0.430570 | − | 0.902557i | \(-0.641687\pi\) |
0.996922 | − | 0.0783942i | \(-0.0249793\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.62847 | + | 37.5919i | 0.299750 | + | 1.69997i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.1513 | − | 7.69846i | −0.954547 | − | 0.347427i | −0.182652 | − | 0.983178i | \(-0.558468\pi\) |
−0.771894 | + | 0.635751i | \(0.780691\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.38516 | 0.287573 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 30.1913 | 1.35700 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.2645 | − | 6.64772i | −0.819273 | − | 0.298191i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.60596 | − | 26.1217i | −0.206191 | − | 1.16937i | −0.895555 | − | 0.444951i | \(-0.853221\pi\) |
0.689364 | − | 0.724415i | \(-0.257890\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −36.7480 | + | 63.6494i | −1.64178 | + | 2.84364i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.1792 | − | 25.3234i | −1.34563 | − | 1.12911i | −0.980142 | − | 0.198296i | \(-0.936459\pi\) |
−0.365484 | − | 0.930818i | \(-0.619096\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.63352 | + | 6.29345i | 0.161690 | + | 0.280055i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −38.0155 | + | 13.8365i | −1.68833 | + | 0.614500i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.40757 | + | 19.3253i | −0.151038 | + | 0.856578i | 0.811281 | + | 0.584656i | \(0.198771\pi\) |
−0.962319 | + | 0.271922i | \(0.912341\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.79171 | − | 3.18162i | 0.167735 | − | 0.140747i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −48.8052 | + | 12.3198i | −2.15480 | + | 0.543930i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.651497 | − | 0.546671i | 0.0287084 | − | 0.0240892i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.723724 | + | 4.10444i | −0.0318294 | + | 0.180513i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.5117 | + | 11.1053i | −1.33931 | + | 0.487470i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.49964 | − | 14.7218i | −0.372376 | − | 0.644974i | 0.617554 | − | 0.786528i | \(-0.288124\pi\) |
−0.989931 | + | 0.141554i | \(0.954790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.3000 | + | 21.2293i | 1.10629 | + | 0.928291i | 0.997832 | − | 0.0658102i | \(-0.0209632\pi\) |
0.108461 | + | 0.994101i | \(0.465408\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.00566 | + | 3.47390i | −0.0875340 | + | 0.151613i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.964433 | − | 5.46957i | −0.0420114 | − | 0.238258i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.5714 | + | 4.93957i | 0.590059 | + | 0.214764i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 71.7597 | 3.11410 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.972250 | −0.0421128 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.48731 | + | 3.45310i | 0.410172 | + | 0.149290i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.54675 | − | 25.7859i | −0.196207 | − | 1.11274i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.0249 | − | 20.8277i | 0.517947 | − | 0.897111i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.8252 | − | 13.2789i | −0.680378 | − | 0.570905i | 0.235739 | − | 0.971816i | \(-0.424249\pi\) |
−0.916117 | + | 0.400912i | \(0.868693\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 35.1086 | + | 60.8099i | 1.50666 | + | 2.60960i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.82224 | − | 1.02721i | 0.120891 | − | 0.0440009i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.19901 | − | 18.1425i | 0.136780 | − | 0.775717i | −0.836824 | − | 0.547472i | \(-0.815590\pi\) |
0.973604 | − | 0.228245i | \(-0.0732988\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.3228 | − | 25.4438i | 1.29414 | − | 1.08592i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.1474 | − | 16.3902i | 1.02871 | − | 0.698248i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.94057 | + | 2.46743i | −0.125046 | + | 0.104926i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.84733 | − | 27.4906i | 0.205758 | − | 1.16691i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.4882 | − | 11.0968i | 1.29183 | − | 0.470186i | 0.397500 | − | 0.917602i | \(-0.369878\pi\) |
0.894326 | + | 0.447416i | \(0.147656\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.583735 | + | 1.01106i | 0.0246894 | + | 0.0427632i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.2463 | + | 8.59763i | 0.432597 | + | 0.362992i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.29185 | + | 7.43371i | −0.180880 | + | 0.313293i | −0.942180 | − | 0.335106i | \(-0.891228\pi\) |
0.761300 | + | 0.648399i | \(0.224561\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.05304 | − | 5.97211i | −0.0443019 | − | 0.251248i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.1864 | + | 6.98328i | 0.805753 | + | 0.293270i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.8173 | 0.788861 | 0.394431 | − | 0.918926i | \(-0.370942\pi\) | ||||
0.394431 | + | 0.918926i | \(0.370942\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.57993 | −0.400907 | −0.200454 | − | 0.979703i | \(-0.564242\pi\) | ||||
−0.200454 | + | 0.979703i | \(0.564242\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 71.1322 | + | 25.8900i | 2.97159 | + | 1.08157i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.507981 | + | 2.88091i | 0.0211843 | + | 0.120142i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.41220 | − | 11.1063i | 0.266943 | − | 0.462359i | −0.701128 | − | 0.713036i | \(-0.747320\pi\) |
0.968071 | + | 0.250676i | \(0.0806530\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.0880 | + | 9.30396i | 0.460803 | + | 0.386660i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.61944 | + | 9.73316i | 0.233134 | + | 0.403799i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.100892 | − | 0.0367215i | 0.00417850 | − | 0.00152085i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.142638 | − | 0.808941i | 0.00589736 | − | 0.0334456i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.7329 | + | 17.3970i | −0.855739 | + | 0.718050i | −0.961046 | − | 0.276390i | \(-0.910862\pi\) |
0.105307 | + | 0.994440i | \(0.466417\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.6873 | − | 18.2092i | −0.728791 | − | 0.750295i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.6569 | − | 24.0460i | 1.17879 | − | 0.989120i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.90373 | + | 33.4817i | −0.242437 | + | 1.37493i | 0.583933 | + | 0.811802i | \(0.301513\pi\) |
−0.826370 | + | 0.563127i | \(0.809598\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.15382 | + | 0.419954i | −0.0473018 | + | 0.0172164i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.2205 | + | 31.5588i | 0.745714 | + | 1.29161i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.383051 | + | 0.321418i | 0.0156510 | + | 0.0131328i | 0.650580 | − | 0.759438i | \(-0.274526\pi\) |
−0.634929 | + | 0.772571i | \(0.718970\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.43562 | + | 5.95066i | −0.140142 | + | 0.242733i | −0.927550 | − | 0.373699i | \(-0.878089\pi\) |
0.787408 | + | 0.616432i | \(0.211422\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.3762 | + | 104.217i | 0.748336 | + | 4.24402i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.70704 | − | 3.16910i | −0.353991 | − | 0.128842i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.65201 | −0.310586 | −0.155293 | − | 0.987868i | \(-0.549632\pi\) | ||||
−0.155293 | + | 0.987868i | \(0.549632\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −26.8573 | −1.08831 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.106555 | + | 0.0387827i | 0.00431074 | + | 0.00156898i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.77627 | − | 32.7589i | −0.233302 | − | 1.32312i | −0.846161 | − | 0.532927i | \(-0.821092\pi\) |
0.612860 | − | 0.790192i | \(-0.290019\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.3656 | + | 21.4178i | −0.498629 | + | 0.863650i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.5490 | + | 9.69076i | 0.464945 | + | 0.390135i | 0.844947 | − | 0.534851i | \(-0.179632\pi\) |
−0.380002 | + | 0.924986i | \(0.624077\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.4112 | − | 26.6930i | −0.619428 | − | 1.07288i | −0.989590 | − | 0.143914i | \(-0.954031\pi\) |
0.370162 | − | 0.928967i | \(-0.379302\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 31.7443 | − | 11.5540i | 1.27386 | − | 0.463645i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.34560 | + | 18.9738i | −0.134038 | + | 0.760170i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.766044 | − | 0.642788i | 0.0306418 | − | 0.0257115i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 60.8187 | + | 6.21308i | 2.42887 | + | 0.248126i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.54561 | − | 5.49242i | 0.260990 | − | 0.218997i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.76052 | + | 32.6695i | −0.229323 | + | 1.30055i | 0.624924 | + | 0.780685i | \(0.285130\pi\) |
−0.854247 | + | 0.519868i | \(0.825981\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 36.8297 | − | 13.4049i | 1.46385 | − | 0.532798i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.32109 | − | 5.75230i | −0.131794 | − | 0.228273i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.501242 | − | 0.420592i | −0.0198599 | − | 0.0166645i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 50.6217 | − | 87.6793i | 2.00256 | − | 3.46854i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.69073 | − | 20.9312i | −0.145775 | − | 0.826732i | −0.966741 | − | 0.255756i | \(-0.917676\pi\) |
0.820966 | − | 0.570977i | \(-0.193435\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.7776 | − | 15.9338i | −1.72642 | − | 0.628366i | −0.728056 | − | 0.685517i | \(-0.759576\pi\) |
−0.998366 | + | 0.0571513i | \(0.981798\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 29.6970 | 1.16932 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.02896 | 0.158395 | 0.0791974 | − | 0.996859i | \(-0.474764\pi\) | ||||
0.0791974 | + | 0.996859i | \(0.474764\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −45.2636 | − | 16.4746i | −1.77675 | − | 0.646685i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.05660 | + | 23.0061i | 0.158991 | + | 0.901681i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.38069 | + | 11.0517i | −0.249696 | + | 0.432486i | −0.963441 | − | 0.267919i | \(-0.913664\pi\) |
0.713746 | + | 0.700405i | \(0.246997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.06862 | + | 5.93127i | 0.276194 | + | 0.231754i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.8913 | + | 22.3284i | 0.502937 | + | 0.871112i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.6911 | − | 6.43902i | 0.689146 | − | 0.250829i | 0.0263766 | − | 0.999652i | \(-0.491603\pi\) |
0.662770 | + | 0.748823i | \(0.269381\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.07438 | − | 11.7644i | 0.0806842 | − | 0.457583i | −0.917521 | − | 0.397688i | \(-0.869812\pi\) |
0.998205 | − | 0.0598944i | \(-0.0190764\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.278772 | − | 0.233917i | 0.0108266 | − | 0.00908459i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.28550 | + | 4.54994i | −0.127406 | + | 0.176439i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.0040 | + | 12.5899i | −0.580957 | + | 0.487481i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.29544 | + | 41.3745i | −0.282058 | + | 1.59963i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.9680 | + | 9.08760i | −0.963878 | + | 0.350823i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.9605 | + | 20.7161i | 0.461042 | + | 0.798547i | 0.999013 | − | 0.0444155i | \(-0.0141426\pi\) |
−0.537972 | + | 0.842963i | \(0.680809\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.84620 | − | 7.42284i | −0.340490 | − | 0.285705i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.45024 | + | 9.44010i | −0.209470 | + | 0.362812i | −0.951548 | − | 0.307501i | \(-0.900507\pi\) |
0.742078 | + | 0.670314i | \(0.233840\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.88237 | + | 22.0180i | 0.148992 | + | 0.844973i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −61.7996 | − | 22.4932i | −2.36816 | − | 0.861941i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.353548 | −0.0135282 | −0.00676408 | − | 0.999977i | \(-0.502153\pi\) | ||||
−0.00676408 | + | 0.999977i | \(0.502153\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.65261 | −0.139559 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −56.6878 | − | 20.6327i | −2.16278 | − | 0.787186i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.000507251 | − | 0.00287676i | −1.93247e−5 | − | 0.000109596i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.06320 | + | 1.84152i | −0.0404460 | + | 0.0700546i | −0.885540 | − | 0.464564i | \(-0.846211\pi\) |
0.845094 | + | 0.534618i | \(0.179545\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −29.7776 | − | 24.9864i | −1.13116 | − | 0.949153i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.41264 | + | 16.3032i | 0.357042 | + | 0.618415i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.11368 | + | 2.58917i | −0.269450 | + | 0.0980718i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.00202 | − | 5.68274i | 0.0378999 | − | 0.214941i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.4345 | − | 13.7902i | 0.620722 | − | 0.520848i | −0.277308 | − | 0.960781i | \(-0.589442\pi\) |
0.898030 | + | 0.439933i | \(0.144998\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.6555 | − | 37.5733i | 0.401880 | − | 1.41710i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.20957 | − | 1.85405i | 0.0832171 | − | 0.0698274i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.62473 | − | 9.21432i | 0.0611044 | − | 0.346540i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.1314 | − | 14.2427i | 1.46961 | − | 0.534895i | 0.521616 | − | 0.853180i | \(-0.325329\pi\) |
0.947995 | + | 0.318286i | \(0.103107\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.99754 | − | 17.3162i | −0.374937 | − | 0.649410i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.0508 | + | 10.9509i | 0.488756 | + | 0.410115i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.275688 | + | 0.477506i | −0.0103102 | + | 0.0178577i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.5542 | + | 65.5272i | 0.431500 | + | 2.44716i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.1111 | + | 4.04411i | 0.414374 | + | 0.150820i | 0.540790 | − | 0.841157i | \(-0.318125\pi\) |
−0.126416 | + | 0.991977i | \(0.540347\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.09499 | −0.0407797 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.8297 | 0.700285 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.29160 | + | 2.28996i | 0.233664 | + | 0.0850469i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.05821 | + | 6.00138i | 0.0392467 | + | 0.222579i | 0.998123 | − | 0.0612463i | \(-0.0195075\pi\) |
−0.958876 | + | 0.283825i | \(0.908396\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.789882 | − | 1.36812i | 0.0292549 | − | 0.0506709i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.96355 | + | 5.84311i | 0.257556 | + | 0.216115i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.7539 | − | 46.3391i | −0.988177 | − | 1.71157i | −0.626867 | − | 0.779126i | \(-0.715663\pi\) |
−0.361310 | − | 0.932446i | \(-0.617670\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15.6403 | + | 5.69262i | −0.576902 | + | 0.209975i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.3350 | − | 69.9551i | 0.454365 | − | 2.57683i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.9031 | − | 19.2180i | 0.842504 | − | 0.706945i | −0.115621 | − | 0.993293i | \(-0.536886\pi\) |
0.958126 | + | 0.286348i | \(0.0924415\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.453809 | − | 1.60021i | 0.0166711 | − | 0.0587853i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.6959 | + | 30.7915i | −1.34624 | + | 1.12963i | −0.366268 | + | 0.930510i | \(0.619365\pi\) |
−0.979975 | + | 0.199122i | \(0.936191\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.04509 | − | 11.5983i | 0.0749264 | − | 0.424929i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −55.0116 | + | 20.0226i | −2.01277 | + | 0.732588i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.49952 | − | 11.2575i | −0.237487 | − | 0.411340i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.4465 | + | 16.3175i | 0.709611 | + | 0.595434i | 0.924490 | − | 0.381206i | \(-0.124491\pi\) |
−0.214879 | + | 0.976641i | \(0.568936\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.81448 | + | 6.60688i | −0.139008 | + | 0.240768i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.20517 | + | 6.83485i | 0.0438606 | + | 0.248746i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.9241 | − | 9.07161i | −0.905880 | − | 0.329713i | −0.153274 | − | 0.988184i | \(-0.548982\pi\) |
−0.752607 | + | 0.658470i | \(0.771204\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −41.0291 | −1.48926 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.9695 | 1.55764 | 0.778822 | − | 0.627244i | \(-0.215817\pi\) | ||||
0.778822 | + | 0.627244i | \(0.215817\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.63369 | − | 1.32255i | −0.131548 | − | 0.0478797i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.11062 | − | 6.29865i | −0.0401546 | − | 0.227728i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.655265 | + | 1.13495i | −0.0236602 | + | 0.0409807i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.0908 | − | 30.2838i | −1.30147 | − | 1.09206i | −0.989890 | − | 0.141839i | \(-0.954698\pi\) |
−0.311577 | − | 0.950221i | \(-0.600857\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.7776 | + | 27.3277i | 0.568217 | + | 0.984182i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.4768 | + | 7.45294i | −0.736499 | + | 0.268064i | −0.682913 | − | 0.730499i | \(-0.739287\pi\) |
−0.0535859 | + | 0.998563i | \(0.517065\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.01129 | − | 5.73531i | 0.0363266 | − | 0.206018i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −27.5321 | + | 23.1022i | −0.987710 | + | 0.828787i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.2563 | + | 28.0520i | −0.725756 | + | 1.00507i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −52.0599 | + | 43.6834i | −1.86285 | + | 1.56312i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.4261 | − | 76.1430i | 0.479808 | − | 2.72113i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.4053 | + | 5.97103i | −0.585530 | + | 0.213115i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.0963 | − | 41.7360i | −0.858940 | − | 1.48773i | −0.872941 | − | 0.487826i | \(-0.837790\pi\) |
0.0140010 | − | 0.999902i | \(-0.495543\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −26.3254 | − | 22.0896i | −0.937210 | − | 0.786412i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.90391 | + | 6.76177i | −0.138807 | + | 0.240421i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.125531 | + | 0.711922i | 0.00445774 | + | 0.0252811i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.0698241 | − | 0.0254139i | −0.00247640 | − | 0.000901338i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.8798 | 0.810443 | 0.405221 | − | 0.914219i | \(-0.367194\pi\) | ||||
0.405221 | + | 0.914219i | \(0.367194\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.882911 | 0.0312352 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −94.3049 | − | 34.3242i | −3.33210 | − | 1.21279i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.00524 | − | 17.0436i | −0.106053 | − | 0.601455i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.88322 | − | 3.26184i | 0.0663748 | − | 0.114965i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 47.6385 | + | 39.9735i | 1.67696 | + | 1.40713i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.54829 | − | 9.60992i | −0.195068 | − | 0.337867i | 0.751855 | − | 0.659328i | \(-0.229159\pi\) |
−0.946923 | + | 0.321461i | \(0.895826\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.68468 | − | 1.70509i | 0.164502 | − | 0.0598737i | −0.258457 | − | 0.966023i | \(-0.583214\pi\) |
0.422958 | + | 0.906149i | \(0.360992\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.07914 | − | 17.4627i | 0.107990 | − | 0.612443i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.38566 | + | 7.87550i | −0.328765 | + | 0.275867i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 41.3335 | + | 4.22252i | 1.44608 | + | 0.147727i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.810164 | + | 0.679808i | −0.0283094 | + | 0.0237544i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.09160 | + | 23.2046i | −0.142798 | + | 0.809847i | 0.826311 | + | 0.563214i | \(0.190435\pi\) |
−0.969109 | + | 0.246633i | \(0.920676\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.1290 | − | 14.9697i | 1.43367 | − | 0.521812i | 0.495687 | − | 0.868501i | \(-0.334916\pi\) |
0.937980 | + | 0.346689i | \(0.112694\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.01269 | + | 12.1463i | 0.244151 | + | 0.422881i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.73462 | − | 5.65102i | −0.234186 | − | 0.196505i | 0.518141 | − | 0.855295i | \(-0.326624\pi\) |
−0.752327 | + | 0.658790i | \(0.771069\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.3329 | + | 28.2894i | −0.567264 | + | 0.982530i | 0.429571 | + | 0.903033i | \(0.358665\pi\) |
−0.996835 | + | 0.0794970i | \(0.974669\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.4046 | − | 98.7064i | −0.603759 | − | 3.42409i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.78751 | − | 1.74251i | −0.165877 | − | 0.0603745i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.5902 | −0.816372 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −67.2524 | −2.32458 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.5786 | + | 6.76204i | 0.641403 | + | 0.233452i | 0.642187 | − | 0.766548i | \(-0.278027\pi\) |
−0.000783927 | 1.00000i | \(0.500250\pi\) | ||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.74854 | + | 15.5877i | 0.0947771 | + | 0.537508i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.9688 | − | 36.3190i | 0.722204 | − | 1.25089i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.94709 | − | 8.34660i | −0.342190 | − | 0.287132i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.96498 | + | 10.3316i | 0.204959 | + | 0.354999i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.0490 | − | 8.02519i | 0.756721 | − | 0.275424i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.55142 | + | 25.8124i | −0.156021 | + | 0.884838i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.0634 | − | 21.8698i | 0.892394 | − | 0.748808i | −0.0762946 | − | 0.997085i | \(-0.524309\pi\) |
0.968689 | + | 0.248278i | \(0.0798645\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.3683 | − | 20.9693i | −0.696581 | − | 0.717135i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.9066 | − | 10.8299i | 0.440881 | − | 0.369943i | −0.395158 | − | 0.918613i | \(-0.629310\pi\) |
0.836039 | + | 0.548670i | \(0.184866\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.729186 | + | 4.13542i | −0.0248795 | + | 0.141099i | −0.994717 | − | 0.102653i | \(-0.967267\pi\) |
0.969838 | + | 0.243751i | \(0.0783781\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29.9216 | − | 10.8906i | 1.01972 | − | 0.371149i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.5050 | − | 32.0517i | −0.629919 | − | 1.09105i | −0.987568 | − | 0.157195i | \(-0.949755\pi\) |
0.357649 | − | 0.933856i | \(-0.383579\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.98365 | − | 6.69908i | −0.271452 | − | 0.227775i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25.0653 | + | 43.4143i | −0.851262 | + | 1.47443i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.33065 | + | 13.2178i | 0.0790618 | + | 0.448382i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.81609 | − | 0.661003i | −0.0615359 | − | 0.0223972i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −116.459 | −3.94153 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.28752 | −0.0435261 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.6083 | + | 10.4126i | 0.966032 | + | 0.351607i | 0.776395 | − | 0.630247i | \(-0.217046\pi\) |
0.189638 | + | 0.981854i | \(0.439269\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.4078 | + | 76.0392i | 0.452233 | + | 2.56474i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.10993 | − | 8.85066i | 0.172158 | − | 0.298186i | −0.767016 | − | 0.641628i | \(-0.778259\pi\) |
0.939174 | + | 0.343442i | \(0.111593\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.8764 | − | 17.5174i | −0.702548 | − | 0.589508i | 0.219949 | − | 0.975511i | \(-0.429411\pi\) |
−0.922497 | + | 0.386003i | \(0.873855\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.6680 | + | 28.8698i | 0.560289 | + | 0.970449i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −46.7138 | + | 17.0024i | −1.56849 | + | 0.570885i | −0.972662 | − | 0.232223i | \(-0.925400\pi\) |
−0.595832 | + | 0.803109i | \(0.703178\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.48503 | + | 8.42202i | −0.0498063 | + | 0.282466i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 54.6877 | − | 45.8884i | 1.83211 | − | 1.53732i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.33899 | − | 2.26637i | 0.111735 | − | 0.0758411i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.43803 | − | 5.40215i | 0.215199 | − | 0.180574i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.193841 | + | 1.09933i | −0.00647217 | + | 0.0367055i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 36.6410 | − | 13.3362i | 1.22204 | − | 0.444788i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.0113724 | − | 0.0196976i | −0.000378871 | − | 0.000656223i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −29.2901 | − | 24.5773i | −0.974713 | − | 0.817881i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.2689 | + | 19.5183i | −0.374591 | + | 0.648810i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.81396 | − | 21.6301i | −0.126641 | − | 0.718215i | −0.980320 | − | 0.197416i | \(-0.936745\pi\) |
0.853679 | − | 0.520799i | \(-0.174366\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 45.7977 | + | 16.6690i | 1.51901 | + | 0.552875i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.97667 | −0.231148 | −0.115574 | − | 0.993299i | \(-0.536871\pi\) | ||||
−0.115574 | + | 0.993299i | \(0.536871\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.2963 | 1.30052 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.2796 | + | 6.28926i | 0.571246 | + | 0.207917i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.06303 | − | 11.7000i | −0.0681271 | − | 0.386368i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.179981 | + | 0.311736i | −0.00593702 | + | 0.0102832i | −0.868979 | − | 0.494850i | \(-0.835223\pi\) |
0.863042 | + | 0.505133i | \(0.168556\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 41.1278 | + | 34.5103i | 1.35521 | + | 1.13715i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.924491 | + | 1.60127i | 0.0304300 | + | 0.0527063i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.41948 | − | 3.06444i | 0.276831 | − | 0.100758i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.990439 | − | 5.61706i | 0.0325303 | − | 0.184488i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.16646 | − | 7.69157i | 0.300742 | − | 0.252352i | −0.479911 | − | 0.877317i | \(-0.659331\pi\) |
0.780653 | + | 0.624965i | \(0.214887\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.5783 | + | 5.69937i | −0.739973 | + | 0.186789i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.1674 | − | 16.9224i | 0.660250 | − | 0.554016i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.745502 | + | 4.22795i | −0.0243805 | + | 0.138269i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.8842 | − | 9.78505i | 0.878269 | − | 0.319664i | 0.136758 | − | 0.990604i | \(-0.456332\pi\) |
0.741511 | + | 0.670941i | \(0.234110\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.30050 | + | 3.98458i | 0.0750740 | + | 0.130032i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.4644 | + | 12.9762i | 0.504126 | + | 0.423012i | 0.859057 | − | 0.511881i | \(-0.171051\pi\) |
−0.354930 | + | 0.934893i | \(0.615495\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.6107 | − | 20.1104i | 0.378098 | − | 0.654884i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.58183 | + | 14.6423i | 0.0839868 | + | 0.476313i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.2743 | + | 7.01526i | 0.626330 | + | 0.227965i | 0.635633 | − | 0.771991i | \(-0.280739\pi\) |
−0.00930331 | + | 0.999957i | \(0.502961\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.470861 | −0.0152848 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.98196 | −0.226405 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.9752 | + | 16.3696i | 1.45689 | + | 0.530265i | 0.944507 | − | 0.328492i | \(-0.106540\pi\) |
0.512384 | + | 0.858756i | \(0.328762\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.21909 | + | 23.9276i | 0.136526 | + | 0.774280i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −46.9527 | + | 81.3244i | −1.51776 | + | 2.62885i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.60256 | + | 3.02291i | 0.116333 | + | 0.0976148i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.45823 | − | 2.52573i | −0.0470398 | − | 0.0814752i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 63.6271 | − | 23.1584i | 2.05036 | − | 0.746268i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.806749 | + | 4.57530i | −0.0259702 | + | 0.147284i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.80608 | + | 8.22828i | −0.315342 | + | 0.264604i | −0.786696 | − | 0.617341i | \(-0.788210\pi\) |
0.471354 | + | 0.881944i | \(0.343766\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.941086 | − | 12.9168i | −0.0302320 | − | 0.414949i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.5441 | − | 18.0776i | 0.691381 | − | 0.580138i | −0.227926 | − | 0.973679i | \(-0.573194\pi\) |
0.919307 | + | 0.393541i | \(0.128750\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.20887 | − | 23.8697i | 0.134930 | − | 0.765227i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.358578 | − | 0.130512i | 0.0114837 | − | 0.00417972i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.66796 | + | 13.2813i | 0.245320 | + | 0.424906i | 0.962221 | − | 0.272268i | \(-0.0877737\pi\) |
−0.716902 | + | 0.697174i | \(0.754440\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 51.6042 | + | 43.3011i | 1.64928 | + | 1.38391i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0711 | − | 17.4437i | 0.321546 | − | 0.556933i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.27909 | + | 29.9392i | 0.168377 | + | 0.954913i | 0.945514 | + | 0.325582i | \(0.105560\pi\) |
−0.777137 | + | 0.629331i | \(0.783329\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.2831 | + | 4.10671i | 0.359510 | + | 0.130851i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.71370 | −0.118208 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.8842 | −0.886665 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.16155 | − | 2.24262i | −0.195728 | − | 0.0712392i | 0.242296 | − | 0.970202i | \(-0.422099\pi\) |
−0.438024 | + | 0.898963i | \(0.644322\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.46782 | − | 8.32445i | −0.0465800 | − | 0.264168i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.84826 | + | 10.1295i | −0.185402 | + | 0.321126i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.92015 | − | 2.45030i | −0.0924821 | − | 0.0776017i | 0.595374 | − | 0.803448i | \(-0.297004\pi\) |
−0.687856 | + | 0.725847i | \(0.741448\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −51.7335 | − | 89.6051i | −1.63678 | − | 2.83498i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 380.2.u.b.101.3 | ✓ | 18 | |
19.4 | even | 9 | 7220.2.a.w.1.1 | 9 | |||
19.15 | odd | 18 | 7220.2.a.y.1.9 | 9 | |||
19.16 | even | 9 | inner | 380.2.u.b.301.3 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.u.b.101.3 | ✓ | 18 | 1.1 | even | 1 | trivial | |
380.2.u.b.301.3 | yes | 18 | 19.16 | even | 9 | inner | |
7220.2.a.w.1.1 | 9 | 19.4 | even | 9 | |||
7220.2.a.y.1.9 | 9 | 19.15 | odd | 18 |